Lyapunov Functional Method for 1D Radiative and Reactive Viscous Gas Dynamics |
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Authors: | Email author" target="_blank">Bernard?DucometEmail author Alexander?Zlotnik |
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Institution: | (1) DPTA/Service de Physique Nucléaire, CEA/DAM Ile de France, BP 12, F–91680 Bruyères-le-Châtel, France;(2) Department of Mathematical Modelling, Moscow Power Engineering Institute, Krasnokazarmennaya 14, 111250 Moscow, Russia |
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Abstract: | We consider the compressible Navier–Stokes system for 1D-flows of a viscous heat-conducting gas, with the pressure law and a one-order kinetics to include radiative effects and reactive processes. The mass force and the ignition phenomenon are also taken into account. For large data and under general assumptions on the heat conductivity, we establish global-in-time bounds and exponential stabilization for solutions in Lq and H1 norms. To this end, we construct new global Lyapunov functionals and show that they describe the dynamics of solutions for any t≧0. A short proof of the corresponding global existence is also included for completeness. |
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